Rewrite as a simplified fraction. ${3.4\overline{8} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 348.8888...\\ 10x &= 34.8888...\end{align*}}$ Subtracting the two equations, we have: ${90x = 314}$ ${x = \dfrac{314}{90}} $ ${x = \dfrac{157}{45}} \text{or} {3 \dfrac{22}{45}}$